Question

A sample of 120 students in a high school reveals a mean height of 1.62 meters and a standard deviation of 7 centimeters.

Find 90% and 99% confidence intervals for the true mean height of the student population.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 162 cm.

sample standard deviation = s = 7 cm.

sample size = n = 120

Degrees of freedom = df = n - 1 = 120 - 1 = 119

1) At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t_{0.05, 119} = 1.658

Margin of error = E = t_/2,df * (s /n)

= 1.658 * ( 7/ 120)

Margin of error = E = 1.06

The 99% confidence interval estimate of the population mean is,

  ± E  

= 162 ± 1.06

= (160.94 cm., 163.06 cm.)

2) At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t_{0.005, 119} = 2.618

Margin of error = E = t_/2,df * (s /n)

= 2.618 * ( 7/ 120)

Margin of error = E = 1.67

The 99% confidence interval estimate of the population mean is,

  ± E  

= 162 ± 1.67

= (160.33 cm., 163.67 cm.)